On Rapid Periodic Variations of Terrestrial Magnetism. 



A. 



9P 



tg ér = 



21 



V 





'+1, 



.^ +«% 



tg Ç-^'^= ^f_2 « . 



■(>) 



(^) 



It may Ije seen that 



A,^ JZ,„ 



wbicli varies from 1/« to «, and tlien fr(.)ni « to ]/«, when ? in- 

 creases from to 1 and 1 to go . The phase difference is given by 





tgfs^'.x-vg= 



(i+F)^ 



(9) 



If c<l, then ^^-^ 

 If |<1, then c'' -''- 



or <::90" according as «>- or <:1. 

 ç'^ <i or >90'* according as «>» or «c:!. 



Thus we see in this case that the phase difference as well 

 as the ratio of the amplitudes may assume different values according 

 to the values of « and ?. If the effect of the induced current be 

 taken into account, these values wdll of course be altered 

 considerably. Fig. 22 illustrates the variation of the amplitude 

 ratio and phase difference as functions of ç for a special case. 



In the above discussion, /- was considered constant. If it 

 varies at the same time, the results will be more complicated, in 

 some cases giving rise to a higher harmonic oscillation of the 

 magnetic field. In the case treated in § 22, the external source 

 of the disturbance was such as could be represented by the wave- 

 like distril)ution of current in a ßxed horizontal layer. If such 

 current layer is disturbed into a wave motion simutaneous with 

 the fluctuation of the intensity, each elementary current will be 

 subjected to motion similar to that expressed by (1) of this 

 paragraph. This motion will greatly modify the relations between 

 the X- and Z-component waves discussed in the preceding paragraph 

 as is suggested by the al)ove simple example. It seems plausible 



